[tex]\displaystyle\bf\\\left \{ {{4(x-y)^{2} +7(x-y)=15} \atop {2x+5y=1}} \right.[/tex]

Решим первое уравнение системы заменив x - y = m .

[tex]\displaystyle\bf\\4m^{2} +7m-15=0\\\\D=7^{2} -4\cdot 4\cdot(-15)=49+240=289=17^{2} \\\\\\m_{1} =\frac{-7-17}{8} =-3\\\\\\m_{2} =\frac{-7+17}{8}=1,25[/tex]

Вернёмся к системе :

[tex]\displaystyle\bf\\1)\\\\\left \{ {{x-y=-3} \ |\cdot(-2) \atop {2x+5y=1}} \right. \\\\\\+\left \{ {{-2x+2y=6} \atop {2x+5y=1}} \right.\\ ---------\\7y=7\\\\y=1\\\\x=y-3=1-3=-2\\\\\\2)\\\\\left \{ {{x-y=1,25} \ |\cdot(-2) \atop {2x+5y=1}} \right. \\\\\\+\left \{ {{-2x+2y=2,5} \atop {2x+5y=1}} \right.\\----------\\7y=3,5\\\\y=0,5\\\\x=y+1,25=0,5+1,25=1,75\\\\\\Otvet \ : \ (-2 \ ; \ 1) \ , \ (1,75 \ ; \ 0,5)[/tex]